I'm not a Mini owner, but I'm coming here looking for help! I'm doing a K conversion myself soon and need a taller final drive. The tallest one readily available is 4.059, which is still much too short with tiny wheels. Good luck getting any traction before 4th gear, and get used to 5000+ rpm on the highway.

John Frana (johnfrana@yahoo.com) sells a custom 3.4 final drive for K series transmissions, and it's compatible with all 5 and 6 speed transmissions. He has them made to-order, but the smallest batch he does is 3. They're $1200 each with 3 buyers. Prices may be lower with more. Please post here and shoot him an email if you're interested!

I'm reaching out on a few other forums where K swaps are commonly done, to see just how many we can get in on this.